A storage system typically comprises one or more storage devices into which data may be entered, and from which data may be obtained, as desired. The storage system may be implemented in accordance with a variety of storage architectures including, but not limited to, a network-attached storage environment, a storage area network and a disk assembly directly attached to a client or host computer. The storage devices are typically disk drives, wherein the term “disk” commonly describes a self-contained rotating magnetic media storage device. The term “disk” in this context is synonymous with hard disk drive (HDD) or direct access storage device (DASD).
The disks within a storage system are typically organized as one or more groups, wherein each group is operated as a Redundant Array of Independent (or Inexpensive) Disks (RAID). Most RAID implementations enhance the reliability/integrity of data storage through the redundant writing of data “stripes” across a given number of physical disks in the RAID group, and the appropriate storing of redundant information with respect to the striped data. The redundant information enables recovery of data lost when a storage device fails.
In the operation of a disk array, it is anticipated that a disk can fail. A goal of a high performance storage system is to make the mean time to data loss (MTTDL) as long as possible, preferably much longer than the expected service life of the system. Data can be lost when one or more disks fail, making it impossible to recover data from the device. Typical schemes to avoid loss of data include mirroring, backup and parity protection. Mirroring is an expensive solution in terms of consumption of storage resources, such as disks. Backup does not protect data modified since the backup was created. Parity schemes are common because they provide a redundant encoding of the data that allows for a single erasure (loss of one disk) with the addition of just one disk drive to the system.
Parity protection is used in computer systems to protect against loss of data on a storage device, such as a disk. A parity value may be computed by summing (usually modulo 2) data of a particular word size (usually one bit) across a number of similar disks holding different data and then storing the results on an additional similar disk. That is, parity may be computed on vectors 1-bit wide, composed of bits in corresponding positions on each of the disks. When computed on vectors 1-bit wide, the parity can be either the computed sum or its complement; these are referred to as even and odd parity respectively. Addition and subtraction on 1-bit vectors are both equivalent to exclusive-OR (XOR) logical operations. The data is then protected against the loss of any one of the disks, or of any portion of the data on any one of the disks. If the disk storing the parity is lost, the parity can be regenerated from the data. If one of the data disks is lost, the data can be regenerated by adding the contents of the surviving data disks together and then subtracting the result from the stored parity.
Typically, the disks are divided into parity groups, each of which comprises one or more data disks and a parity disk. A parity set is a set of blocks, including several data blocks and one parity block, where the parity block is the XOR of all the data blocks. A parity group is a set of disks from which one or more parity sets are selected. The disk space is divided into stripes, with each stripe containing one block from each disk. The blocks of a stripe are usually at the same locations on each disk in the parity group. Within a stripe, all but one block are blocks containing data (“data blocks”) and one block is a block containing parity (“parity block”) computed by the XOR of all the data. If the parity blocks are all stored on one disk, thereby providing a single disk that contains all (and only) parity information, a RAID-4 implementation is provided. If the parity blocks are contained within different disks in each stripe, usually in a rotating pattern, then the implementation is RAID-5. The term “RAID” and its various implementations are well-known and disclosed in A Case for Redundant Arrays of Inexpensive Disks (RAID), by D. A. Patterson, G. A. Gibson and R. H. Katz, Proceedings of the International Conference on Management of Data (SIGMOD), June 1988.
As used herein, the term “encoding” means the computation of a redundancy value over a predetermined subset of data blocks, whereas the term “decoding” means the reconstruction of a data or parity block by the same process as the redundancy computation using a subset of data blocks and redundancy values. If one disk fails in the parity group, the contents of that disk can be decoded (reconstructed) on a spare disk or disks by adding all the contents of the remaining data blocks and subtracting the result from the parity block. Since two's complement addition and subtraction over 1-bit fields are both equivalent to XOR operations, this reconstruction consists of the XOR of all the surviving data and parity blocks. Similarly, if the parity disk is lost, it can be recomputed in the same way from the surviving data.
Parity schemes generally provide protection against a single disk failure within a parity group. These schemes can also protect against multiple disk failures as long as each failure occurs within a different parity group. However, if two disks fail concurrently within a parity group, then an unrecoverable loss of data is suffered. Failure of two disks concurrently within a parity group is a fairly common occurrence, particularly because disks “wear out” and because of environmental factors with respect to the operation of the disks. In this context, the failure of two disks concurrently within a parity group is referred to as a “double failure”.
A double failure typically arises as a result of a failure of one disk and a subsequent failure of another disk while attempting to recover from the first failure. The recovery or reconstruction time is dependent upon the level of activity of the storage system. That is, during reconstruction of a failed disk, it is possible that the storage system remain “online” and continue to serve requests (from clients or users) to access (i.e., read and/or write) data. If the storage system is busy serving requests, the elapsed time for reconstruction increases. The reconstruction process time also increases as the size and number of disks in the storage system increases, as all of the surviving disks must be read to reconstruct the lost data. Moreover, the double disk failure rate is proportional to the square of the number of disks in a parity group. However, having small parity groups is expensive, as each parity group requires an entire disk devoted to redundant data.
Another failure mode of disks is media read errors, wherein a single block or sector of a disk cannot be read. The unreadable data can be reconstructed if parity is maintained in the storage array. However, if one disk has already failed, then a media read error on another disk in the array will result in lost data. This is a second form of double failure.
Accordingly, it is desirable to provide a technique that withstands double failures. This would allow construction of larger disk systems with larger parity groups, while ensuring that even if reconstruction after a single disk failure takes a long time (e.g., a number of hours), the system can survive a second failure. Such a technique would further allow relaxation of certain design constraints on the storage system. For example, the storage system could use lower cost disks and still maintain a high MTTDL. Lower cost disks typically have a shorter lifetime, and possibly a higher failure rate during their lifetime, than higher cost disks. Therefore, use of such disks is more acceptable if the system can withstand double disk failures within a parity group.
It can easily be shown that the minimum amount of redundant information required to correct a double failure is two units. Therefore, the minimum number of parity disks that can be added to the data disks is two. This is true whether the parity is distributed across the disks or concentrated on the two additional disks.
A known double failure correcting parity scheme is an EVENODD XOR-based technique that allows a serial reconstruction of lost (failed) disks. EVENODD parity requires exactly two disks worth of redundant data, which is optimal. According to this parity technique, all disk blocks belong to two parity sets, one a typical RAID-4 style XOR computed across all the data disks and the other computed along a set of diagonally adjacent disk blocks. The diagonal parity sets contain blocks from all but one of the data is disks. For n data disks, there are n−1 rows of blocks in a stripe. Each block is on one diagonal and there are n diagonals, each n−1 blocks in length. Notably, the EVENODD scheme only works if n is a prime number. The EVENODD technique is disclosed in an article of IEEE Transactions on Computers, Vol. 44, No. 2, titled EVENODD: An Efficient Scheme for Tolerating Double Disk Failures in RAID Architectures, by Blaum et al, February, 1995. A variant of EVENODD is disclosed in U.S. Pat. No. 5,579,475, titled Method and Means for Encoding and Rebuilding the Data Contents of up to Two Unavailable DASDs in a DASD Array using Simple Non-Recursive Diagonal and Row Parity, by Blaum et al., issued on Nov. 26, 1996. The above-mentioned article and patent are hereby incorporated by reference as though fully set forth herein.
The EVENODD technique utilizes a total of p+2 disks, where p is a prime number and p disks contain data, with the remaining two disks containing parity information. One of the parity disks contains row parity blocks. Row parity is calculated as the XOR of all the data blocks that are at the same position in each of the data disks. The other parity disk contains diagonal parity blocks. Diagonal parity is constructed from p−1 data blocks that are arranged in a diagonal pattern on the data disks. The blocks are grouped into stripes of p−1 rows. This does not affect the assignment of data blocks to row parity sets. However, diagonals are constructed in a pattern such that all of their blocks are in the same stripe of blocks. This means that most diagonals “wrap around” within the stripe, as they go from disk to disk.
Specifically, in an array of n×(n−1) data blocks, there are exactly n diagonals each of length n−1, if the diagonals “wrap around” at the edges of the array. The key to reconstruction of the EVENODD parity arrangement is that each diagonal parity set contains no information from one of the data disks. However, there is one more diagonal than there are blocks to store the parity blocks for the diagonals. That is, the EVENODD parity arrangement results in a diagonal parity set that does not have an independent parity block. To accommodate this extra “missing” parity block, the EVENODD arrangement XOR's the parity result of one distinguished diagonal into the parity blocks for each of the other diagonals.
FIG. 1 is a schematic block diagram of a prior art disk array 100 that is configured in accordance with the conventional EVENODD parity arrangement. Each data block Dab belongs to parity sets a and b, where the parity block for each parity set is denoted Pa. Note that for one distinguished diagonal (X), there is no corresponding parity block stored. This is where the EVENODD property arises. In order to allow reconstruction from two failures, each data disk must not contribute to at least one diagonal parity set. By employing a rectangular array of n×(n−1) data blocks, the diagonal parity sets have n−1 data block members. Yet, as noted, such an arrangement does not have a location for storing the parity block for all the diagonals. Therefore, the parity of the extra (missing) diagonal parity block (X) is recorded by XOR'ing that diagonal parity into the parity of each of the other diagonal parity blocks. Specifically, the parity of the missing diagonal parity set is XOR'd into each of the diagonal parity blocks P4 through P7 such that those blocks are denoted P4X–P7X.
For reconstruction from the failure of two data disks, the parity of the diagonal that does not have a parity block is initially recomputed by XOR'ing all of the parity blocks. For example, the sum of all the row parities is the sum of all the data blocks. The sum of all the diagonal parities is the sum of all the data blocks minus the sum of the missing diagonal parity block. Therefore, the XOR of all parity blocks is equivalent to the sum of all the blocks (the row parity sum) minus the sum of all the blocks except the missing diagonal, which is just a parity of the missing diagonal. Actually, n−1 copies of the missing diagonal parity are added into the result, one for each diagonal parity block. Since n is a prime number greater than two, n−1 is even, resulting in the XOR of a block with itself an even number of times, which results in a zero block. Accordingly, the sum of the diagonal parity blocks with the additional missing parity added to each is equal to the sum of the diagonal parity blocks without the additional diagonal parity.
Next, the missing diagonal parity is subtracted from each of the diagonal parity blocks. After two data disks fail, there are at least two diagonal parity sets that are missing only one block. The missing blocks from each of those parity sets can be reconstructed, even if one of the sets is the diagonal for which there is not a parity block. Once those blocks are reconstructed, all but one member of two of the row parity sets are available. This allows reconstruction of the missing members of those rows. This reconstruction occurs on other diagonals, which provides enough information to reconstruct the last missing blocks on those diagonals. The pattern of reconstructing alternately using row then diagonal parity continues until all missing blocks have been reconstructed.
Since n is prime, a cycle is not formed in the reconstruction until all diagonals have been encountered, hence all the missing data blocks have been reconstructed. If n were not prime, this would not be the case. If both parity disks are lost, a simple reconstruction of parity from data can be performed. If a data disk and the diagonal parity disk are lost, a simple RAID-4 style reconstruction of the data disk is performed using row parity followed by reconstruction of the diagonal parity disk. If a data disk and the row parity disk are lost, then one diagonal parity may be computed. Since all diagonals have the same parity, the missing block on each diagonal can subsequently be computed.
Since each data block is a member of a diagonal parity set, when two data disks are lost (a double failure), there are two parity sets that have lost only one member. Each disk has a diagonal parity set that is not represented on that disk. Accordingly, for a double failure, there are two parity sets that can be reconstructed. EVENODD also allows reconstruction from failures of both parity disks or from any combination of one data disk and one parity disk failure. The technique also allows reconstruction from any single disk failure.
Although the EVENODD technique is optimal in terms of the amount of parity information, the amount of computation required for both encoding and decoding is only asymptotically optimal. This is because of the extra computation required to add the missing diagonal parity into each of the diagonal parity blocks. That is, the p−1 blocks in a stripe are not enough to hold the p parity blocks generated from the p diagonals. To overcome this, the EVENODD technique requires that the parity of one of the diagonals be XOR'd into the parity blocks of all the other diagonals, thereby increasing computational overhead.
In general, all diagonal parity blocks must be updated for any small write operation to a data block along the diagonal that has no direct parity block. Extra computation is also needed for a large write operation. As used herein, a “large-write” operation involves rewriting of all the blocks of a stripe, whereas a “small-write” operation involves modification of at least one data block and its associated parity.